According to Kuichling’s empirical relation, the required fire-demand Q (in L/min) for a town of population P (in thousands) is given by which expression?

Introduction: Fire-demand formulas provide a quick estimate of the rate at which water must be supplied for firefighting. Kuichling’s is a classic empirical relation used in many water-supply design problems and competitive examinations.

Given Data / Assumptions:

• P denotes population in thousands (dimensionless in the formula).
• Q is desired in litres per minute (L/min).

Concept / Approach: Kuichling derived a square-root dependence of fire demand on town size, reflecting that firefighting requirements scale sublinearly with population. The metric version widely quoted is Q = 3182 * sqrt(P), with Q in L/min and P in thousands.

Step-by-Step Solution: Identify the correct dependence: Q ∝ sqrt(P), not linear in P. Select the metric coefficient 3182 for L/min units. Form the expression Q = 3182 * sqrt(P).

Verification / Alternative check: Imperial versions expressed in gal/min convert to the metric coefficient near 3182 when multiplied by 3.785; the square-root scaling remains the hallmark of the formula.

Why Other Options Are Wrong:

• 5663 * sqrt(P), 2050 * sqrt(P): Incorrect coefficients for the stated units.
• 3182 * P and 1136 * P: Wrong dependence (linear in P instead of square-root).

Common Pitfalls:

• Using P as absolute population rather than in thousands.
• Mixing imperial and metric constants without conversion.

Final Answer: Q = 3182 * sqrt(P).